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Unformatted text preview: 74 CHAPTER 1. COORDINATES AND VECTORS upward diagonal. We denote the determinant by replacing the brackets surrounding the array with vertical bars: 13 vextendsingle vextendsingle vextendsingle vextendsingle x 1 y 1 x 2 y 2 vextendsingle vextendsingle vextendsingle vextendsingle = x 1 y 2 − x 2 y 1 . It is also convenient to sometimes treat the determinant as a function of its rows, which we think of as vectors: −→ v i = x i −→ ı + y i −→ , i = 1 , 2; treated this way, the determinant will be denoted Δ( −→ v 1 , −→ v 2 ) = vextendsingle vextendsingle vextendsingle vextendsingle x 1 y 1 x 2 y 2 vextendsingle vextendsingle vextendsingle vextendsingle . If we are simply given the coordinates of the vertices of a triangle in the plane, without a picture of the triangle, we can pick one of the vertices—call it A —and calculate the vectors to the other two vertices—call them B and C —and then take half the determinant. This will equal the area of the triangle...
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
 Fall '08
 ALL
 Calculus, Determinant, Vectors

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